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A039825
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a(n) = floor((n^2 + n + 8) / 4).
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0
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2, 3, 5, 7, 9, 12, 16, 20, 24, 29, 35, 41, 47, 54, 62, 70, 78, 87, 97, 107, 117, 128, 140, 152, 164, 177, 191, 205, 219, 234, 250, 266, 282, 299, 317, 335, 353, 372, 392, 412, 432, 453, 475, 497, 519, 542, 566, 590, 614, 639
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OFFSET
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1,1
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COMMENTS
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Number of different coefficient values in expansion of Product_{i=1..n} (1 + q^2 + q^4 + ... + q^(2i)).
The given terms have a second difference that is periodic with the period 1, 0, 0, 1, ... of length 4, an implicit recurrence. - John W. Layman, Jan 23 2001
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LINKS
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FORMULA
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O.g.f.: -x*(2*x^4 - 4*x^3 + 4*x^2 - 3*x + 2)/((x-1)^3*(x^2+1)). - R. J. Mathar, Dec 05 2007
a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5). - Wesley Ivan Hurt, May 08 2022
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PROG
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(Magma) [Floor((n^2+n+8)/4): n in [1..50]]; // Bruno Berselli, Jul 25 2012
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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